JP2002162328A - Method for introducing structural formula of material by indentation test - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for introducing a structural formula from an indentation force versus depth curve which specifies the force deformation behavior of a material. SOLUTION: The structural formula to be determined which includes N unknown numbers is hypothesized for the surface of the material, and a hypothetical numerical experiment relating to the indentation test is carried out for the material as the object. Then, a characteristic curve representing the relationship between the N unknown numbers and N values of apparent hardness obtained from differential indenters with N kinds of forms is determined using numerical analysis such as finite element method. The apparent hardness is experimentally determined from the indentation force versus depth curve using the N indenters, and constant numbers in the structural formula can be determined from the relationship between the N values of apparent hardness being measured and the characteristic curve obtained above.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for deriving a constitutive equation for defining a load deformation behavior of a material (an equation for defining a material-specific deformation behavior with respect to a load) from an indentation load-indentation depth curve. It is.

[0002]

2. Description of the Related Art With respect to a constitutive equation for defining the load deformation behavior of a material, except for Young's modulus, information obtained from an indentation test is based on the relationship between hardness or semiempirical hardness and yield stress. It was limited to the case where it was evaluated on a regular basis.
A method has been established for obtaining this Young's modulus from the relationship between the indentation load unloading and the indentation depth.

[0003]

Conventionally, qualitative information obtained from an indentation test is evaluated as quantitative information,
It is an object of the present invention to derive a constitutive equation that can describe the load deformation behavior of a material indispensable for engineering design.

[0004]

An indentation load-indentation curve of a target material is obtained by a plurality of indenters having different shapes corresponding to the number of unknown constants included in the material constitutive expression to be obtained. That is, a curve for several indenters (the number of unknown constants in the constitutive equation) is obtained. Evaluate the apparent hardness from each load and depth curve, and calculate each constant in the constitutive equation from the relationship between the characteristic curve obtained from numerical analysis by the finite element method etc. on the apparent hardness and the actually measured apparent hardness. To decide.

[0005]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A virtual numerical experiment on an indentation test is performed on a material surface including N unknowns and on the assumption of a constitutive equation to be determined, and N values obtained from N indenters having different shapes are obtained. A characteristic curve representing a relationship between the apparent hardness and the N unknowns is obtained by numerical analysis using a well-known finite element method or the like.

Next, the apparent hardness is experimentally determined from the indentation load-indentation depth curve by the N indenters, and the configuration is determined from the relationship between the actually measured N apparent hardness and the previously determined characteristic curve. This is a method that can determine the constants in the equation.

That is, as shown in FIG. 2, in order to determine a material constitutive equation fc including a plurality (N) of unknown constants representing a deformation behavior with respect to a load, which is inherent to the material,
The indentation load / depth-depth curve using the indenter is obtained.

First, in evaluating the characteristics of a material surface, as shown in FIG. 2, virtual numerical experiments using a computer were performed on each of N indenters having different shapes (i = 1, i, N). Is performed, the indentation load / depth-depth curve of the material is obtained numerically. Based on each of these curves, the equivalent hardness (apparent hardness) S shown in the left diagram of FIG. 1 is obtained using a well-known finite element analysis (see FIG. 3). For the apparent hardness Si obtained for the N indenters, the unknown constant C for the material in the material constitutive equation as shown in FIG.
Regarding the relationship of i, a characteristic curve as shown in FIG. 3 is obtained by numerical analysis.

Next, an indentation load experiment was actually performed on the material surface using N different indenters having the same shape as described above, and an indentation load / depth-depth curve of the material was obtained. From this curve, apparent hardnesses Si, S1, and SN for each indenter were obtained.

The experimentally obtained apparent hardness S1,
Inserting Si, SN into the equation as shown in FIG. 3 to obtain unknown constant Ci. Then, the obtained N numerical values are numerically different from the obtained numerical values from the characteristic curve relating to Ci, which is an unknown constant with respect to the apparent hardness Si, obtained by numerical analysis in FIG. Verify that there is no

As the indenter having a different shape used in the present invention, a triangular pyramid indenter having a different apex angle as shown in FIG. 1 is used, and the indenter is pressed into the surface of the sample material.
The indentation load / depth-depth curve shown in FIG. 1 is obtained.

[0012]

First, as a material constitutive equation capable of expressing the load displacement behavior of a nickel-base alloy, an exponential function type constitutive equation shown in FIG. 4 is assumed. In the exponential function type formula, there are four unknown constants to be determined. That is, Young's modulus E (elastic coefficient), yield stress (σy), work hardening index n, work hardening coefficient A. Here, the Young's modulus can be obtained from a conventional indentation load / depth-depth curve.

Therefore, as shown in FIG.
One unknown must be determined. Therefore, according to the present invention, indenters having three different shapes are prepared. Here, a triangular pyramid indenter with a different apex angle (equivalent cone apex angle: 63 degrees,
70 degrees, 76 degrees).

First, a virtual numerical experiment according to each of the three indenter shapes is performed by a general-purpose finite element method code DYNA. Then, an indentation load / depth-depth curve was obtained by numerical analysis, and a relationship between each triangular pyramid indenter and apparent hardness was obtained as a characteristic curve for an arbitrary constant.

Next, an apparent hardness was actually measured from an indentation load / depth-depth curve by three indenters by an experiment. From the measured apparent hardness and the characteristic curve, the yield stress σy, the work hardening index n,
The work hardening coefficient A was determined.

The usefulness of the present invention could be confirmed because the uniaxial tensile load-displacement curve analytically evaluated by introducing the determined constitutive equation well represented the experimentally evaluated load-displacement curve.

[0017]

In particular, when the indentation area is small, the present method is effective as an application to a micro test technique. Specifically, it can be expected to be applied as a material property evaluation method for radiation irradiation materials, thin film coating materials, corrosion surface layers, and the like.

[Brief description of the drawings]

FIG. 1 is a diagram showing indenters having different shapes and indentation load / depth-depth curves using the indenters.

FIG. 2 is a diagram showing a material constitutive equation including a plurality of unknown constants and an indentation load / depth-depth curve obtained from a plurality of indenters.

FIG. 3 is a diagram showing a method for deriving a material constitutive equation.

FIG. 4 is a diagram showing an example of deriving a material constitutive equation.

 ──────────────────────────────────────────────────続 き Continuing from the front page (72) Inventor Ikuo Ioka 2-4, Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki Pref. Niigata University

Claims (3)

[Claims] 1. A method for deriving a material constitutive equation for evaluating a material surface property from an indentation test using a plurality of indenters having different shapes. 2. A method for deriving a material constitutive equation by fusing an indentation load-indentation depth curve obtained from a plurality of indenters having different shapes and a characteristic curve obtained from numerical analysis. 3. A method of deriving a material constitutive equation by an indentation test, comprising the steps of: a) performing a virtual numerical experiment with a computer on a plurality of indenters having different shapes corresponding to the number of unknown constants in the material constitutive equation to indent the material; A load-indentation depth curve is obtained numerically; b) an apparent hardness (equivalent hardness) is obtained by a well-known finite element method analysis (FEM) based on each of the curves; c) the obtained apparent value A characteristic curve is obtained for the relationship between the hardness and the yield stress, work hardening coefficient, work hardening index, etc., which are unknown constants in the material constitutive equation. C) The same three types of different indenters having different shapes are used for the material surface. The indentation test was actually performed to obtain an indentation load-indentation depth curve of the material, and from this curve, the apparent hardness of each indenter was obtained. The hardness is inserted into the material constitutive equation to obtain unknown constants, such as yield stress, work hardening coefficient and work hardening index. E) The numerical value obtained by the actual measurement is converted into the characteristic obtained by the above numerical analysis. Verifying numerical approximation by comparing with a numerical value obtained from a curve.